MRI systems use the nuclear magnetic resonance (NMR) effects that RF transmissions at the nuclei Lamor frequency have on atomic nuclei having a net magnetic moment such as those in hydrogen. The net magnetic moment of these nuclei are first magnetically aligned by a strong static magnetic field B.sub.0 (e.g., typically created by magnetic poles on opposite sides of the MRI imaging volume or inside a solenoidal cryogenic superconducting electromagnet). The static field B.sub.0 is altered by gradient magnetic fields created in the X, Y, and Z directions of the imaging volume. Selected nuclei, which spin in alignment with the B.sub.0 field, are then nutated by the perpendicular magnetic field of a NMR RF transmission at the Lamor frequency, causing a population of such nuclei to tip from the direction of the magnetic field B.sub.0. Thus, for example, in FIG. 1, certain nuclei (designated by magnetic moment M.sub.0) are aligned with the "Z'" axis by the static B.sub.0 field and then rotated to the X'-Y' plane as a result of an RF signal being imposed on them. The nuclei then precess in the X'-Y' plane as shown by the circulating arrow in FIG. 1 (which is a reference frame rotating at the nominal Lamor resonance frequency around the Z' axis).
The NMR RF spin-nutating signal will, of course, tip more than one species of the target isotope in a particular area. Immediately after the nutating RF signal tips them, the spinning nuclei will all be in-phase with each other; that is, the rotating magnetic moments of all NMR species all rotate across the "Y'" axis all at approximately the same time. However, after the NMR nutating RF pulse ends, each species of nuclei begin to freely precess at its own characteristic speed around the Z' axis. As they do, the phase of the rotating nuclei species will differ as a result of such parameters as the physical or chemical environment that the nuclei are located in. Nuclei in fat, for example, precess at a different rate than do nuclei in water. In an MRI imaging pulse sequence there are also magnetic field gradients which dephase the moments due to their local resonance frequency varying in space.
Once the spins are disturbed from their equilibrium, processes known as relaxation cause the phase-coherent component of magnetic moments in the X'-Y' plane to decay and the Z'-component to recover to its equilibrium magnitude, M.sub.0. These processes are usually characterized by exponentials whose time constants are called T.sub.2 and T.sub.1, respectively. When magnetic resonance signals are observed through flux oscillation in a plane coexistent with the X'-Y' plane, both of these processes decrease the signal strength as a function of time.
As a result, if the relative phase of components of the magnetic moments in the X'-Y' plane of FIG. 1 begin aligned on the Y'-axis, over time they will begin to spread out and disperse to fill the full rotational area. The nuclei of moment M.sub.2, for example, which initially crossed the Y'-axis at the same time as M.sub.0, gradually moves during the relaxation period to the position shown in FIG. 1 as it spins faster than M.sub.0. M.sub.1, by contrast, spins slower than both M.sub.0 and M.sub.2, and thus begins to lag them during the dephasing period. The strength of the detectable NMR response signal thus decays as the relative phases of the magnetic moments disperse (i.e., lose phase coherence) in the X'-Y' plane.
Information about NMR hydrogen nuclei can be obtained, in part, by measuring their T.sub.2, T.sub.1 decay times. In addition, before the nuclei become completely dephased another RF signal (e.g., a 180.degree. signal) can tip the magnetic moments (e.g., to a 180.degree. inverted position). This inverts the spinning magnetic moments M.sub.0, M.sub.1 and M.sub.2 so the fastest moment M.sub.2 now lags (instead of leading) M.sub.0, which in turn also now lags the slowest moment M.sub.1. Eventually, the faster moment M.sub.2 will again catch up with and pass the slowest moment M.sub.1 during which, a so-called "spin-echo" NMR RF response can be detected from the changes in net magnetic moment as the various magnetic moments come back into phase coherence. The whole procedure must, of course, be completed before T.sub.1 or T.sub.2 relaxation processes destroy the detectable X'-Y' components of the magnetic moments.
Detectable NMR RF response echoes can also be formed by application of a field gradient and it's subsequent reversal, provided that it is done before T.sub.1 or T.sub.2 relaxation destroy M.sub.X'Y'. This is commonly called a field echo, gradient echo or race-track echo.
The above are just two background examples of how the nuclei can be tipped, relaxed, brought in- or out-of-phase, etc. from which information about the nuclei can be obtained by observing detectable NMR RF response signals.
The differences in the phase relationships between the species of nuclei in one tissue versus another can be used as information to separate MRI images of fat components of tissue from fluids or water-based tissue (for these purposes, "water-based tissue" and "fluids" are used interchangeably).
Although MR images of both water and fat may contain the same or different diagnostic information, they often interfere with each other's interpretation when overlapped in an MRI image and thus make it difficult to properly interpret the composite MR image. Somewhat different diagnostic information may also be obtained from separate MR images of only the fat-based or water-based species of NMR nuclei.
At high field strengths, the separation of water and fat images or suppression of fat signals can be achieved using selective excitation or non-excitation approaches. However, at mid- or low field strengths, approaches based on chemical shift selectivity become impractical, if not impossible. At all field strengths, the difficulties of water/fat image separation are further exacerbated when there are large magnetic field inhomogeneities.
This difficulty in separating fat and water images in a practical MR imaging application is particularly true for mid- and low-field systems where the frequency separation between the water and fat signals is much reduced in comparison to that at high fields. Recently, several techniques were introduced for separation of water and fat images in the presence of large field inhomogeneities. Some of these techniques use multiple spin-echoes, thus requiring the use of multiple RF refocusing pulses. They are therefore sensitive to magnetic field inhomogeneities and also preclude multiple-echo experiments. The Three-Point Dixon method has promising features for mid- or low field applications. It uses a single spin-echo sequence but relies on the acquisition of three images for water/fat separation, an in-phase image and two out-phase images. Unfortunately, it requires a minimum of three scans to do so.
FIG. 2 shows the three data acquisition schemes for the three images in the Three-Point Dixon method. Slice selection is not shown for simplicity. As those in the art will understand from FIG. 2, three different scans are used. In the first, a 90.degree. pulse is followed by a 180.degree. pulse at a time T, yielding the spin echo S.sub.0. Then, a 90.degree. pulse is followed by a 180.degree. pulse a time .tau. earlier than the time T, yielding a spin echo S.sub..pi.. Finally, another 90.degree. pulse is followed by a 180.degree. pulse a time .tau. later than the time T, yielding a spin echo S.sub.-.pi.. The Dixon Methodology is described in "Three-Point Dixon Technique for True Water Fat Decompositions with B.sub.0 Inhomogeneity Corrected,"18 Magnetic Resonance in Medicine, 371-383 (1991), by Glover et al., "True Water and Fat MR Imaging With Use of Multiple-Echo Acquisition", 173 Radiology 249-253 (1989), by Williams et al., "Separation of True Fat and Water Images By Correcting Magnetic Field Inhomogeneity In Situ," 159 Radiology 783-786 (1986), by Yeung et al., which are incorporated herein by reference, and are summarized in part below.
The value of .tau. is determined according to .tau.=1/(4.DELTA..nu.) with .DELTA..nu. being the frequency difference between the water and fat signals. The value of .tau. is thus chosen so the phase between the nuclei in, respectively, fat and water are 1) in-phase, 2) out-of-phase by .pi., and 3) out-of-phase by -.pi.. FIGS. 3a, 3b and 3c schematically show in a rotating frame the MR signals in the three different acquisition schemes.
Other phase differences than .pi. can also be used as described in Hardy et al., JMRI, 1995. Additionally, the S.sub.0 signal could be derived from a gradient reversal induced field echo. It is not required that S.sub.0 be an RF induced spin echo.
In a brief summary, three NMR RF responses are required to compute separate water-based and fat-based images:
S.sub.0 =a first NMR response with phase coherent fat and water NMR species; PA1 S.sub..theta. =a second NMR response with a predetermined difference between fat and water NMR species in a first (e.g., "positive") direction; and PA1 S.sub.-.theta. =a third NMR response with the same predetermined phase difference between fat and water NMR species in the opposite (e.g., "negative") direction. PA1 1) fitting the phase derivatives to polynomial functions; and PA1 2) phase unwrapping. PA1 (A) A pixel in the image was chosen as the subseed for unwrapping and the measured phase value was assigned to the final phase value used for water and fat image reconstruction. EQU .phi..sub.f (x.sub.0,y.sub.0)=.phi.(x.sub.0,y.sub.0) PA1 (B) From the subseed, a 4.times.4 seed was built by comparing the phase values to the subseed value. If the difference is larger than a predetermined threshold, a 2.pi. unwrapping is executed: EQU .DELTA..phi.=.phi.-.phi.(x.sub.0,y.sub.0) EQU .phi..sub.f =.phi.+sign(.DELTA..phi.).times.2.PI. PA1 (C) Continuing from the seed, a four column cross is built using a single direction prediction: EQU .phi..sub.p =1/4 {.phi..sub.f.sup.-.spsp.4 +.phi..sub.f.sup.-.spsp.3 +.phi..sub.f.sup.-.spsp.2 .phi..sub.f.sup.-.spsp.1 +4.delta..phi..sup.-.spsp.1 +3.delta..phi..sup.-.spsp.2 +2.delta..phi..sup.-.spsp.3 +.delta..phi..sup.-.spsp.4 } EQU .DELTA..phi.=.phi.-.phi..sub.p PA1 (D) Using the cross, the four quadrants of the image are unwrapped using the same prediction approach, but in two directions. Unwrapping is executed when both directions show the same execution for unwrapping. In other situations, the average of the predicted values is used. When the pixel value is below the intensity threshold, the phase value is again set to the predicted average value.
Once S.sub.0, S.sub..theta., S.sub.-.theta. and .crclbar. are known, then separate MR images of the NMR fat species and/or the NMR water species can be derived. The following more specific description of an exemplary embodiment is based on the .crclbar.=.pi. example detailed in the Dixon paper.
In the presence of field inhomogeneities, the MR signals can be described by EQU S.sub.0 =(P.sub.w +P.sub.f) EQU S.sub..pi. =(P.sub.w -P.sub.f).sup.e.spsp.i.phi. EQU S.sub.-.pi. =(P.sub.w -P.sub.f).sup.e.spsp.-i.phi.
where .phi. is the phase angle due to field inhomogeneities or frequency offset, and P.sub.w and P.sub.f are water and fat spin densities, respectively.
Thus .phi. can be determined from S.sub..pi. and S.sub.-.pi. by EQU .phi.=1/2arg(S.sub..pi.. S*.sub.-.pi.)
where arg produces the phase angle of a complex number.
Water and fat images can then be reconstructed according to EQU I.sub.water =S.sub.0 +0.5S.sub..pi. e.sup.-i.phi. +0.5S.sub.-.pi. e.sup.i.phi. EQU I.sub.fat =S.sub.0 -0.5S.sub..pi. e.sup.-i.phi. -0.5S.sub.-.pi. e.sup.i.phi .
The central component of this method--and also the most demanding component to determine--is the phase angle .phi.. The phase angle is generally determined by phase mapping. Calculating .phi. from S.sub..pi. and S.sub.-.pi. involves:
Each of these are discussed in turn below.
i. Polynomial fitting
The magnetic field is modeled using a polynomial function: ##EQU1##
To find the coefficients a.sub.n and b.sub.n, partial spatial derivatives of the phase value .phi. are calculated and fit to the polynomial functions: ##EQU2## Fitting was performed with weighted least-square with the weighting factors determined according to ##EQU3## where S.sub.0 (x,y) is the pixel value in the in-phase image and S.sub.0max is the maximum of that image.
From p.sub.n and q.sub.n, a.sub.n and b.sub.n are calculated from the equations: ##EQU4## ii. Binary Phase Unwrapping
If it can be assumed that the magnetic field fitting is relatively accurate within a small error range, for example, .+-.0.2.pi., then unwrapping can be performed by simply comparing the measured phase .phi. with the predicted phase .phi..sub.p : EQU .DELTA..phi.=.phi..sub.p -.phi.
If .vertline..DELTA..phi..vertline.&gt;.pi., then .phi..sub.f used for water and fat image reconstruction is determined by ##EQU5## where integer truncates the resulting quotient to whole number. iii. Unwrapping by Region Growing
However, the field fitting may contain large errors (for example, &gt;.pi.) which will cause errors in phase unwrapping and consequently result in water/fat mutual contamination in the final images. To unwrap in a more fool-proof way, a region growing algorithm was implemented as the following:
where .phi..sub.f.sup.-1 (i=1, . . . 4) are unwrapped phase values of the neighboring pixel, .delta..phi..sup.-1 (i=1, . . . 4) are phase increments between two neighboring pixels from the polynomial fitting.
If the pixel value is smaller than the intensity threshold, .phi..sub.f is set to .phi..sub.p. Otherwise, if .vertline..DELTA..phi..vertline.&lt;.pi. set .phi..sub.f to .phi.. If .vertline..DELTA..phi..vertline.&gt;.pi. then EQU .phi..sub.f =.phi.+integer(.delta..phi./2.pi.).times.2.pi..
See Szamowski et al., Radiology 192, page 555-561, 1994 for more discussion of region growing approaches to phase correction.
iv. Results
Shown in FIG. 4 are head images reconstructed with binary phase unwrapping. The left image of FIG. 4 is a water and fat image; the middle image is water only; and the right image is fat only. The corresponding images reconstructed using the region growing algorithms are shown in FIG. 5. FIGS. 6 and 7 show the abdominal images reconstructed in the same way as for FIGS. 3a-3c and FIG. 4, respectively.
As can be seen, this prior method obtains separate fat and water images but disadvantageously requires three separate data acquisition scans (e.g., 3 TR intervals) to obtain them.